I have 2 daughters aged 29 and 27 and a son 22. The girls have always been very selfish. I threw the eldest out at 25 because of her abuse and then the next one too at the same age after she assaulted me as well. My husband of 30 years died 6 years ago and I had cancer 3 years ago. Their bad behaviour continued after their father died and whilst I was ill and my daughters turned my son against me with their lies and he left home when I was having a cancer operation. They could not have been crueller at a worse time in my life.
I have now met a lovely man who I have married and my children are now saying that the reason for them not wanting me is because I remarried.
I honestly gave them my best and I feel terribly betrayed by them.
I don't want this to continue with us not talking but I no longer trust them and have done nothing to deserve this.
They are not going to have anymore to do with me.
My question is how do I learn to live without them?
I am so depressed by it all.

If there is no way to repair the relationship then I would say you have to accept the fact that you have to live your own life without them in it.
Enjoy your life with your husband and know that you did the best you could.
If they are cruel and abusive ,it would seem to me that you would not want that in your life.
I would concentrate on your husband and yourself and maybe in time,if they grow up and turn their selfish ways around they will see the error in their thinking.

I think that now you are enjoying a new life without the 'children', and your new husband, I can see where you might not want to compromise your happiness.

You deserve the life you have, and it is good that you are enjoying it.

That being said, I think you might regret not putting out the olive branch here. What would be wrong with thinking about having the three of them over on your terms, at your convenience.

Maybe define the terms such as barbecue at 4 sharp, no discussions about the past, keep it light and enjoyable.

If you can start with just a little bit, maybe once a month, letting them know what you expect of them, would it be possible for all of you to get together that way?

There will always be room for one on one time down the road after you have built up a good relationship with them again, if you choose to go that route with them.

I'm thinking it would be a shame to totally block them out of your life. Time marches on, and you cannot back it up if you change your mind some day. There may be grandchildren in the future as well; do you want to risk estrangement from them as well?

Maybe they have, or are, growing up a bit now that they are on their own. If it were me, I'd chance occasional visits without any great expectations, but better to try, then wonder 'what if'.